Question

How do we achieve very low temperatures with gas refrigeration cycles?

Short answer

Answer: Gas refrigeration cycles, such as the reverse Brayton cycle, can achieve very low temperatures by undergoing a series of thermodynamic processes, including adiabatic compression, isothermal cooling, adiabatic expansion, and isothermal heating of a working fluid, typically a high heat capacity gas. Achieving very low temperatures requires a high adiabatic efficiency of the reverse Brayton cycle, which can be improved by minimizing pressure drop, optimizing the expansion turbine design, and reducing friction and heat transfer. Another effective method to achieve low temperatures with gas refrigeration cycles is by using cascade refrigeration, where multiple refrigeration cycles with different working fluids are connected in series and operate in different temperature ranges, allowing for significant temperature reduction.

Step-by-step solution

Understand Gas Refrigeration Cycles

Gas refrigeration cycles, such as the reverse Brayton cycle, are thermodynamic cycles used to achieve low temperatures by removing heat from a system using a working fluid, typically a gas. The cycle consists of several stages, including compression, cooling, expansion, and heating.

Explain the Reverse Brayton Cycle

The reverse Brayton cycle is an important gas refrigeration cycle that can be used to achieve low temperatures. It consists of the following four processes: 1. Adiabatic compression of the working fluid, typically a high heat capacity gas like helium or nitrogen, where temperature increases. 2. Isothermal cooling of the compressed gas, where it rejects heat to the surroundings or a cooling medium, such as water or air. 3. Adiabatic expansion of the cooled gas in an expansion turbine, where work is extracted, and the gas temperature significantly drops. 4. Isothermal heating of the expanded gas, where it absorbs heat from the system to be cooled and returns to its initial state, thereby completing the cycle.

Adiabatic Efficiency of the Cycle

Achieving very low temperatures requires a high adiabatic efficiency of the reverse Brayton cycle. Adiabatic efficiency is the ratio of the actual work done by the expansion turbine to the ideal work achievable in a perfect adiabatic process. Improving the adiabatic efficiency can be done by minimizing pressure drop, optimizing the design of the expansion turbine, and reducing friction and heat transfer.

Cascade Refrigeration

Another effective method to achieve very low temperatures with gas refrigeration cycles is by using cascade refrigeration. In this approach, multiple refrigeration cycles are connected in series, with each cycle operating in a different temperature range. The low-temperature cycle extracts heat from the system to be cooled, while the higher-temperature cycle pre-cools the working fluid of the low-temperature cycle. This allows for significant temperature reduction by taking advantage of the more favorable thermodynamic properties of different working fluids in each temperature range.